= Ballistic exhaust interception condition
{title2=$v_A-u_0<v_B$}
For exhaust moving freely from a rocket A toward a collector B behind it along a common axis, the exhaust must overtake B in the rearward direction. At negligible separation and flight time this gives the displayed condition. In the ideal simultaneous-collection solution, write $a=m_A+M-q$, $b=m_B+q$ and $v_A=u_0\ln[(m_A+M)/a]$, $v_B=-av_A/b$. The criterion becomes $[(a+b)/b]\ln[(m_A+M)/a]<1$. A formal endpoint obtained by assuming all fuel is collected need not satisfy this interception test throughout a large burn.
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